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Numerical solution of a two‐dimensional time‐independent Schrödinger equation by using symplectic schemes
Author(s) -
Liu XueShen,
Su LiWei,
Liu XiaoYan,
Ding PeiZhu
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.1063
Subject(s) - symplectic geometry , eigenvalues and eigenvectors , mathematics , harmonic oscillator , schrödinger equation , hamiltonian (control theory) , mathematical analysis , numerical analysis , mathematical physics , quantum mechanics , physics , mathematical optimization
Symplectic schemes are extended to the solution of a two‐dimensional time‐independent Schrödinger equation. The Schrödinger equation is first transformed into a Hamiltonian canonical equation and then the numerical method is developed to solve the numerical solution of the two‐dimensional time‐independent Schrödinger equation. This called the symplectic scheme–matrix eigenvalue method (SSMEM). This method is applied to calculations of the two‐dimensional harmonic oscillator and the two‐dimensional Henon–Heils potential. It is shown that the numerical results of the two‐dimensional harmonic oscillator by using the SSMEM tend to the exact ones monotonically with decreasing space step length and the numerical eigenvalues of the two‐dimensional Henon–Heils potential by using the SSMEM are lower than those by using the Gaussian basis set method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 303–309, 2001